Dispersion Relation and Stability Analysis of Flow-Induced Wave of a Flexible Circular Ring Subjected to Swirling Fluid Flow

Abstract

This paper deals with a theoretical stability analysis of unstable wave generated in a flexible circular ring subjected to swirling fluid flow. The flexible circular ring is set in a rotating circular outer casing with a narrow gap filled with fluid and is subjected to the swirling fluid flow caused by the rotation of the outer casing. In the stability analysis, a wave equation is derived from the equation of motion of the flexible circular ring coupled with the swirling fluid flow. The equation of motion of the flexible circular ring is based on the Kirchhoff-Love’s thin-shell model, and the equations of motion of the swirling fluid flow are based on the Navier-Stokes equations. Moreover, the dispersion relation of the wave generated in the flexible circular ring is derived from the wave equation as a function of the rotational speed of the outer casing. The analytical results show that an unstable wave occurs as a type of traveling forward wave due to the swirling fluid flow when the rotational speed of the outer casing becomes high, and that the most unstable wave mode, phase speed (traveling-wave speed), and growth rate of the wave vary greatly with increasing rotational speed of the outer casing.